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Chapter 1: Problem 65

Decide whether each statement is true or false. $$ -5<-2 $$

Short Answer

Expert verified
-5 < -2 is true.

Step by step solution

01

- Understand the Inequality

The given inequality is ame{-5 < -2}. We need to determine if this statement is true or false.
02

- Compare the Numbers

Compare ame{-5} and ame{-2} on the number line. Remember, on the number line, any number to the left is less than any number to the right.
03

- Analysis on the Number Line

Since ame{-5} is located to the left of ame{-2} on the number line, it is indeed less than ame{-2}.
04

- Conclusion

The inequality ame{-5 < -2} is true because ame{-5} is less than ame{-2}.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Comparing Numbers
When comparing numbers, you need to understand the value of each number. In this exercise, we are comparing -5 and -2. Negative numbers can sometimes be confusing because they represent values less than zero.
  • The larger the negative number, the smaller its value.
  • For instance, -5 is smaller than -2 because -5 is further from zero.
Always think of numbers in their relation to zero: the further left you go, the smaller the number.
Number Line
A number line is a useful tool for visualizing and comparing numbers. It helps you easily see which number is greater or smaller.
  • On the number line, numbers to the left are smaller than those to the right.
  • For example, -5 is located to the left of -2, showing that -5 is indeed smaller.
Visualizing numbers on a number line makes it easier to compare and understand their values. This method is particularly helpful with negative numbers, which are less intuitive for many students.
Inequality Analysis
Inequality analysis is about understanding and verifying statements like -5 < -2.
  • An inequality expresses that one number is either less than, greater than, or equal to another.
  • In our example, we are checking if -5 is less than -2.
By placing these numbers on a number line, you can visually confirm that -5 is to the left of -2. Therefore, -5 < -2 is a true statement.
Analyzing inequalities involves both understanding the numerical values and using visual aids like number lines for confirmation.

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Most popular questions from this chapter

Simplify each expression. $$ -\frac{5}{6}+8 x+\frac{1}{6} x-7-\frac{7}{6} $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ \left(\frac{1}{3} x-\frac{4}{5} y\right)\left(-\frac{1}{5} a\right) $$

Write a numerical expression for each phrase and simplify. The quotient of \(-12\) and the sum of \(-5\) and \(-1\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. 6 less than a number is 4

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ \frac{x y+8 a}{x-y} $$
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